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What Is a Catenary Curve and How Do We Build One in FreeCAD?

The catenary curve (also known as a chainette) comes from the Latin word catenaria, meaning “chain.” This type of curve naturally occurs when a uniform flexible material, like a rope, chain, or cable, hangs freely under its own weight between two supports.

In everyday life and engineering, the catenary shape appears in:

  • Hanging chains

  • Overhead cables

  • Suspension elements

  • Spider webs and vines in nature

It distributes weight evenly between its two ends, forming a mathematically predictable and stable arc.

The Challenge: Modeling a Catenary in FreeCAD

At the time of writing, FreeCAD does not provide a built-in tool to generate a catenary curve with a single click. The only earlier implementation came via the now-discontinued Animation Workbench, where animation paths were used as geometry.

My goal is to explore how we might generate a catenary using FreeCAD's Curves Workbench by plotting a set of points and applying interpolation or approximation techniques to build the curve. Once created, the curve could then serve as a path in other workbenches like Draft or Lattice2, ideal for object arrays or structural modeling.

If anyone has an existing solution for this, please let me know, I’d be happy to add a reference or link here.

R&D: Simplifying the Problem

To approach this, I’ve broken the challenge into manageable steps.

Phase 1 – Proof of Concept

  1. Manually create 2D points (using Draft or Sketch workbench) and test with the Curves Workbench to see if a valid path can be generated.

  2. Repeat this process using a Python script to generate the same point set.

  3. Research and find an equation to compute catenary coordinates. As this is a classical math problem, resources in other programming languages are available and can be adapted.

  4. Integrate the equation into a FreeCAD macro to automate the plotting of the curve.

Phase 2 – Refinement and Expansion

Once the 2D version is proven to work:

  • How can this be expanded into 3D space?

  • What happens if one support is higher than the other?

  • How do different support distances affect the curve’s depth?

These are questions I hope to explore in future updates.

Resources and References

Here are some excellent starting points for understanding and coding the catenary curve:

These will be invaluable as I translate the logic into FreeCAD-compatible Python code.

Final Thoughts

Modeling a catenary curve in FreeCAD is both a mathematical and practical challenge. With the help of scripting, community resources, and FreeCAD’s flexible architecture, it’s entirely possible to create accurate and usable versions of these natural shapes.

If you're experimenting with structural curves, cables, or even artistic elements in FreeCAD, this could open up a range of creative possibilities.

Stay tuned for the macro and future updates, and if you’re working on something similar, feel free to connect.


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